The working condition of spiral bevel gear pair can be simulated in computer by properly preprocessing the finite element mesh model of spiral bevel gear and controlling the speed of driving gear and the resistance moment of driven gear. The specific analysis steps are as follows:
(1) Define material properties
Defining material properties in ABAQUS is an indirect process, rather than directly defining material properties on units or components. First define the section properties, and then specify the material properties in the defined section properties, so that the specified material properties can be assigned to the corresponding components or units. The material properties commonly used in finite element analysis mainly include density, elastic modulus, Poisson’s ratio, elastoplasticity, coefficient of thermal expansion, orthotropic and anisotropic elasticity. When defining material properties in static analysis, the influence of mass and inertia on the results is not considered, and the material density can not be added. However, the influence of mass and “inertia force” on the results needs to be considered in the dynamic analysis.
(2) Create analysis step
In the meshing analysis of spiral bevel gears, the boundary conditions and loads imposed on the model will change with time. Therefore, in the finite element analysis, it is necessary to divide several time periods according to the actual situation, and define the boundary conditions and load conditions for each time period. One analysis step can express one time period. The initial analysis step and several subsequent analysis steps for applying boundary conditions and load conditions are required for loading analysis. The subsequent analysis steps include two types: general analysis step and linear perturbation analysis step. The contact problem of spiral bevel gear belongs to nonlinear analysis. The general analysis step can be used for both linear analysis and nonlinear analysis. Therefore, static and general analysis steps need to be selected for static contact analysis. In addition, the nloem option should be turned on, that is, the option state of nonlinear effect should be turned on.
ABAQUS software will produce large amount of calculation data during analysis and calculation. In order to save resources and improve computing efficiency, it is not necessary to output all the results in practical application, but only the results that may be needed. Therefore, in the analysis process, especially when the amount of calculation is relatively large, it is necessary to check and modify the output requirements and output frequency of the results to avoid the waste of disk space. In order to ensure the convergence of the initial contact analysis of gear teeth, the analysis process is divided into several analysis steps: in the first analysis step, a small amount of rotation on the axis rotation degree of freedom is applied on the large wheel, and a fully fixed boundary condition is applied on the small wheel to make the two tooth surfaces contact; In the next analysis step, the constraint on the big wheel is deleted and the torque is applied on its axis rotation degree of freedom, so that the contact state analysis under the initial load can be realized; Finally, a certain rotation angle is applied on the degree of freedom of the small wheel along the axis, so that the small wheel can drive the large wheel to rotate.
(3) Define contact
In the process of object contact, the relative position relationship between the contact surfaces in contact with each other changes in the whole analysis process. Therefore, the contact properties between contact surfaces are an important consideration. In the contact properties of tangential action, the relative sliding relationship between contact surfaces is mainly considered and the friction model is selected; In the contact properties of normal action, the gap between two surfaces is mainly considered. In this paper, the penalty function friction model suitable for most contact problems is selected. At the same time, the surface to surface contact type, static contact method and finite slip formula are selected. In ABAQUS, there are two contact slip formulas to deal with the sliding problem between contact surfaces. The reference standard for the selection of these two formulas is the relationship between the element size and the slip between the two contact surfaces. The meshing state of spiral bevel gear studied is the state of continuous contact and separation, and there is a large amount of slip between the tooth surfaces, so the finite slip contact algorithm is selected. Taking the friction coefficient of 10.03 and 0.03 as the reference data, it shows that the relative variation range of the friction coefficient between the teeth is relatively poor, which indicates that the formula of 10.03 and 0.03 is relatively poor. Take the middle friction coefficient value of 0.06.
(4) Create coupling constraints
The spiral bevel gear model selects c3d8r element, and establishes coupling constraints between the reference point and the inner hole surface of the shaft to realize the rotation process of the element around the axis. At the same time, by creating a rigid connection between the shaft hole surface and the reference point, the actual load and constraints of the gear can be loaded on the reference point. In order to realize that two mutually meshing spiral bevel gears can rotate according to their respective axes, a reference point is created on the axes of the two spiral bevel gears, as shown in Figure 3.8. The coupling constraint is constructed between the corresponding inner surface of the gear and the reference point, and the torque on the inner surface of the spiral bevel gear is expressed by the torque on the reference point. At the same time, it is necessary to allow the relative deformation between the parts on the coupling beam surface when the spiral bevel gear is loaded.
(5) Define boundary conditions and load time boundary
In order to obtain good analysis results, the applied load should avoid impact, and the way of smooth loading should be adopted. Violent movement can lead to wrong results. The software has the function of creating smooth amplitude. According to the actual working conditions of spiral bevel gears, fix all degrees of freedom on the reference points of the two spiral bevel gears except the axis rotation degrees of freedom. At the same time, a certain angle is applied on the small wheel reference point, and the torque is applied on the large wheel reference point to define the load. The function of smooth amplitude curve needs to be used when applying the load. In the static analysis, the fluctuation caused by discontinuous loading rate can be avoided through the load amplitude curve.
The static contact analysis of spiral bevel gear is not affected by the speed, which mainly studies the influence of load on its meshing characteristics. In order to obtain the influence of different load conditions on the meshing performance of spiral bevel gear, the loading analysis under three different torque conditions is carried out, and the torque is 2T, t and T / 2 respectively. The T value is 447.5n · m; The selected rotation angle is determined according to the number of dense mesh teeth of spiral bevel gear. The loading time has no practical value in static analysis. The loading time used in this paper is 5S.